A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?
We assume the three toppings must be different.
Three things can be ordered in 6 ways (try this), so in the 336 permutations, there are groups of 6 that amount to the same combination :
So we have to divide the number of permutations by the number of orders to reach the number of combinations:
There are thus 336 : 6 = 56 possibilities for the toppings.
Since we need cheese AND toppings we multiply:
Number of different pizzas: 3 x 56 = 168.
Calculator : if you have the nCr function the answer would be:
3 x 8 nCr 3 = 168